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Mathematics and Financial Economics
Published in: Mathematics and Financial Economics 4/2015

01-10-2015

Funding liquidity, debt tenor structure, and creditor’s belief: an exogenous dynamic debt run model

Authors: Gechun Liang, Eva Lütkebohmert, Wei Wei

Published in: Mathematics and Financial Economics | Issue 4/2015

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Abstract

We propose a unified structural credit risk model incorporating both insolvency and illiquidity risks, in order to investigate how a firm’s default probability depends on the liquidity risk associated with its financing structure. We assume the firm finances its risky assets by mainly issuing short- and long-term debt. Short-term debt can have either a discrete or a more realistic staggered tenor structure. At rollover dates of short-term debt, creditors face a dynamic coordination problem. We show that a unique threshold strategy (i.e., a debt run barrier) exists for short-term creditors to decide when to withdraw their funding, and this strategy is closely related to the solution of a non-standard optimal stopping time problem with control constraints. We decompose the total credit risk into an insolvency component and an illiquidity component based on such an endogenous debt run barrier together with an exogenous insolvency barrier.
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Appendix
Available only for authorised users
Footnotes
1
Optimal capital structural models are regarded as the second generation of structural credit risk models, which were initiated by Leland [18‐20]. Therein the firm defaults when its equity value drops to zero, and the default barrier is determined endogenously by its equity holders. Chen and Kou [8] and Hilberink and Rogers [16] extend this model by introducing jump risk, and recently, [14] extends this framework by including an illiquid debt market.
 
2
The assumption of constant interest rates is imposed to simplify derivations. In reality, different rates not only vary in time, but also move differently, motivating the so called multi-curve modeling (see for example [10]).
 
3
The constant \(\psi \) is the fire-sale rate of the firm fundamental when the firm is in a distressed state, i.e., it represents the amount that can be borrowed by pledging one unit of the risky assets as collateral. For a detailed discussion of how to endogenously determine the fire-sale rate by the leverage of the firm, we refer to [23].
 
4
The probability of the insolvency time \(\tau ^{Ins}\) equal to the terminal time \(T\) is zero, so at the terminal time \(T\) the firm only faces the insolvency risk stemming from the final workout of the firm’s risky project. For this reason the recovery rate \(R\) at time \(T\) is redefined as \(R_T=\min \{1,X_T/(1+l_T)\}\).
 
5
Arifovic et al. [3] study how coordination problems can affect the occurrence of bank runs in controlled laboratory environments.
 
6
Recall that \(R_T=\min \{1, X_T/(1+l_T)\}\) as defined in (4).
 
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Metadata
Title
Funding liquidity, debt tenor structure, and creditor’s belief: an exogenous dynamic debt run model
Authors
Gechun Liang
Eva Lütkebohmert
Wei Wei
Publication date
01-10-2015
Publisher
Springer Berlin Heidelberg
Published in
Mathematics and Financial Economics / Issue 4/2015
Print ISSN: 1862-9679
Electronic ISSN: 1862-9660
DOI
https://doi.org/10.1007/s11579-015-0144-6